basis of monoid of integral vectors

Question

Suppose that $M\in\mathbb{Z}^{n\times k}$ is a matrix of rank $k<n$. How can I obtain a set of vectors $b_1,\ldots,b_k\in\mathbb{Z}^k$ (if exists) such that each row of $M$ is a non-negative integral linear combination of the $b_i$? For instance, if $M=\begin{pmatrix}2\\3\end{pmatrix}$, I want $b_1=(1)$. I assume that this is a computationally difficult question. I would be happy if someone can point me to a software. I don't know how to do this with $\texttt{4ti2}$.